Find the limit of (1-x)^(lnx) as x-- 1

Question

Find the limit of (1-x)^(lnx) as x--> 1

lgbasallote · Answer

let y = (1-x)^lnx
lny = lnx ln(1-x)

anonymous · Answer

yeah that is right

anonymous · Answer

then rewrite as 
$$\frac{\ln(1-x)}{\frac{1}{\ln(x)}}$$ and use l'hopital

lgbasallote · Answer

ahhh LH...a very frustrating method involving so much manipulation and circling

anonymous · Answer

LH is frustrating?! it's makes your life easy.

anonymous · Answer

thanks guys you nailed it =]

lgbasallote · Answer

it's frustating when it circles

anonymous · Answer

if it circles then you are missing some thing

anonymous · Answer

derivative of numerator is 
$$-\frac{1}{1-x}$$ derivative of denominator is 
$$-\frac{1}{x\ln^2(x)}$$ ratio is 
$$\frac{x\ln^2(x)}{1-x}$$

lgbasallote · Answer

also... 0/0 is easy.... i hate (inf - inf) 1^inf and something

anonymous · Answer

x goes to one, get 0/1 so not so bad. limit of the log is 0, limit of the original one is 
$$e^0=1$$ unless i made a mistake

anonymous · Answer

yes you are right 1 is the answer ! =]